Model-based study of a nanowire heating and dynamic axisymmetric necking by surface electromigration

TL;DR

This paper presents a coupled model of thermal and morphological dynamics in a nanowire under electromigration, revealing how temperature spikes influence necking and eventual wire breakage.

Contribution

It introduces a comprehensive model that couples temperature evolution and radius change in electromigrating nanowires, highlighting conditions for stability and instability.

Findings

Temperature spikes occur at the neck during electromigration.

Wire radius and length significantly affect temperature and stability.

Conditions for initial solid state before necking are derived.

Abstract

Axisymmetric solid-state necking of a single-crystal metallic nanowire in a thermal contact with a substrate and subjected to a surface electromigration current is accompanied by a local current crowding and a sharp rise of a resistivity of a wire material in a thinning neck. This results in a temperature spike at the neck, which feedback affects the necking via thermomigration and the temperature-dependent surface diffusivity of the adatoms. A model that incorporates these effects and couples the nonlinear dynamics of a wire temperature and a wire radius for a necking wire is presented. Conditions on the physical parameters are derived that ensure a straight wire is in the solid state prior to an onset of a morphological instability that ultimately breaks a wire via a pinch-off. The impacts of a wire radius and a wire length on the temperature spike at the break junction are studied.